Hello,

I have stan code for Regime Switching Model from Jim Savage site. Here this site:

https://khakieconomics.github.io/2018/02/24/Regime-switching-models.html.

I have an issue in creating the log-likelihood in the generated quantities. I am not sure how to define the target syntax in the generated quantities block.

Here this code.

```
data {
int T;
vector[T] y;
}
parameters {
vector<lower = 0, upper = 1>[2] p;
real<lower = 0> phi;
vector[2] delta;
vector<lower = 0>[2] sigma;
real<lower = 0, upper = 1> xi1_init;
real y_tm1_init;
}
transformed parameters {
matrix[T, 2] eta;
matrix[T, 2] xi;
vector[T] f;
// fill in etas
for(t in 1:T) {
eta[t,1] = exp(normal_lpdf(y[t]| delta[1], sigma[1]));
if(t==1) {
eta[t,2] = exp(normal_lpdf(y[t]| delta[2] + phi * y_tm1_init, sigma[2]));
} else {
eta[t,2] = exp(normal_lpdf(y[t]| delta[2] + phi * y[t-1], sigma[2]));
}
}
// work out likelihood contributions
for(t in 1:T) {
// for the first observation
if(t==1) {
f[t] = p[1]*xi1_init*eta[t,1] + // stay in state 1
(1 - p[1])*xi1_init*eta[t,2] + // transition from 1 to 2
p[2]*(1 - xi1_init)*eta[t,2] + // stay in state 2
(1 - p[2])*(1 - xi1_init)*eta[t,1]; // transition from 2 to 1
xi[t,1] = (p[1]*xi1_init*eta[t,1] +(1 - p[2])*(1 - xi1_init)*eta[t,1])/f[t];
xi[t,2] = 1.0 - xi[t,1];
} else {
// and for the rest
f[t] = p[1]*xi[t-1,1]*eta[t,1] + // stay in state 1
(1 - p[1])*xi[t-1,1]*eta[t,2] + // transition from 1 to 2
p[2]*xi[t-1,2]*eta[t,2] + // stay in state 2
(1 - p[2])*xi[t-1,2]*eta[t,1]; // transition from 2 to 1
// work out xi
xi[t,1] = (p[1]*xi[t-1,1]*eta[t,1] +(1 - p[2])*xi[t-1,2]*eta[t,1])/f[t];
// there are only two states so the probability of the other state is 1 - prob of the first
xi[t,2] = 1.0 - xi[t,1];
}
}
}
model {
// priors
p ~ beta(10, 2);
phi ~ normal(1, .1);
delta ~ normal(0, .1);
sigma ~ cauchy(0, 1);
xi1_init ~ beta(2, 2);
y_tm1_init ~ normal(0, .1);
// likelihood is really easy here!
target += sum(log(f));
}
"
```

Thanks for any help you can provide.